Local non–Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

Isaac H. Kim
Phys. Rev. A 83, 052308 – Published 12 May 2011

Abstract

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

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  • Received 3 January 2011

DOI:https://doi.org/10.1103/PhysRevA.83.052308

©2011 American Physical Society

Authors & Affiliations

Isaac H. Kim

  • Institute of Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

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Issue

Vol. 83, Iss. 5 — May 2011

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